Let $f: R \rightarrow R$ be defined by $f(x) = \frac{1}{x}$ for all $x \in R$. Then $f$ is:

Given that $a, b$ and $c$ are real numbers such that $b^2 = 4ac$ and $a > 0$. The maximal possible set $D \subseteq R$ on which the function $f: D \rightarrow R$ given by $f(x) = \log \{ax^3 + (a+b)x^2 + (b+c)x + c\}$ is defined,is

If the domain of the function $f(x) = \frac{[x]}{1+x^2}$,where $[x]$ is the greatest integer $\leq x$,is $(2, 6)$,then its range is

For $x \in \mathbb{R}$,if $f(x) = \sqrt{\log_{10}\left(\frac{3-x}{x}\right)}$,then the domain of $f$ is

Let $[x]$ denote the greatest integer $\leq x$,where $x \in \mathbb{R}$. If the domain of the real-valued function $f(x) = \sqrt{\frac{|[x]|-2}{|[x]|-3}}$ is $(-\infty, a) \cup [b, c) \cup [4, \infty)$,where $a < b < c$,then the value of $a+b+c$ is:

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection,then $B$ is equal to